The flag is used by Israeli Navy, being a blue flag with white triangle at hoist and blue Magen David in it. Proportions are 2:3.

Zeljko Heimer, 1 April 1996

The Commander of the Navy flag is the Navy Ensign as in FOTW with a device. The device is a sword with an olive branch and an anchor.

Nahum Shereshevsky, 8 May 1998

The plates I copied from Ministry of Defence 1974 are not in color. They are shown in black, white, and gray. (...) The Magen David on the command flags is shown in the same black as the field, while the Magen David on the naval ensign is shown as gray.

Since the day of the Declaration of Independence of Israel (14 May 1948)
and until the first Knesset [parliament] was elected and assembled, Israel was governed by The Provisional Council of State by way of issuing Ordenances and Proclamations. Those proclamations had only temporary force, and were supposed to be adapted into Acts of the Knesset to achieve constant status as forceable legislation.

Such was the case of the Proclamation about the National Flag re-adopted by The Flag and Emblem Act which still is in force and the Proclamation about the Merchant Fleet Flag [i.e. civil ensign] readopted by The Ships (Nationality and Flag) Act, later to be replaced by The Maritime (Vessels) Act.
Those Proclamations (and Ordenances) are not included in the Sefer ha-Hukim Book of Laws, the section of the Reshumot or official gazzete in which new laws are published and were published in Iton Rishmi ('official gazzette') which was soon after replaced by
the Reshumot.

While searching the Iton Rishmi for the proclamation concerning the Merchant Fleet Flag, I stumbled upon another and most interesting proclamation. This proclamation was not adopted by an Act of the Knesset and therefore has no official status today, however it is certainly a guideline. My translation, remarks in brackets:

The Provisional Council of State
Proclamation about the War Fleet Flag

The provisional Council of State hereby proclaims that the flag of the war
fleet of the State of Israel is as drawn and described hereafter:
The flag  its length 180 cm, its width 120 cm, its background dark sky-blue [as in the national flag and civil ensign] with a white triangle with two
equal sides, whose top lies in the centre of the flag and its base coincides with the wide side at the hoist. In the triangle, a Magen David with its centre in the centre of gravity of the triangle, made of six sky-blue stripes forming two equilateral triangles, each stripe 32 cm in length and 3 cm in width.

[drawing]

Provisional Council of State
David Ben-Gurion, Chairman
10 Iyar 5708 (19 May 1948)

Note that the war ensign was adopted and proclaimed only 5 days after the declaration of Independence, while the national flag was adopted and proclaimed only on 28 October 1948.

I was watching some documentary on TV today, when a scene from the early years of Israel was showed, with an unidentified flag. The report was about proclamation on Israeli independence in 1948, and some military parade was shown, where in front of units this flag was carried  very similar to Israeli naval ensign with some device in fly end, much in the way the defacement was made in British tradition. The flag passed away from the screen too fast to recognize the defacement, but I believe it was shaped as a lion in a cricle. I attach a sketch drawing of this . I am quite sure that the defacement was not the one that is in current military flag, and I am not sure if the triangular field had the two stripes or not.

Zeljko Heimer, 20 June 1998

I am no expert on Israeli military flags, but it seems to me that there were no stripes and that would make it the Israeli naval ensign with something in the fly.

Nahum Shereshevsky, 20 June 1998

I searched in my archives and in a wonderful article from Zvi Ruder in Raven, some similar flags are quoted. The lion appear in many military flags and is named the lion of Megiddo. One of the flags or standards of the Israel Defense Forces (IDF) is blue-purple with white triangle with the base in the hoist and within a blue magen star; in the fly a badge (but no the lion; seems a fox). I don't know if that is the lion of Megiddo. This word only remembers me a battle in old times.

Jaume Ollé, 2 July 1998

But the article in Raven did not include the detail of the flag shown in Zeljko Heimer's image.

Phil Nelson, 2 July 1998

I have a copy of the article that Zvi Ruder sent me recently. The illustration there (Fig. 2) is of a lion on a seal found in Megido. The lion on the badge/flag of Central Command represents the Lion of Judea, as in the City of Jerusalem emblem/flag. The Megido lion is not a symbol, the name refers to the artistic form. It might have been the artistic inspiration for the Central Command lion, which is different from the City of Jerusalem lion (the former is passant, the latter is rampant, as much as we can apply heraldic terms here).

The fox is the emblem of Southern Command, representing Samson's Foxes. (To complete the picture, Northern Command has a deer on its emblem). These three animals can be seen in flags/badges of many army units that are associated with the commands. But all of them are ground forces. The flag that Zeljko Heimer sent looks like a Navy flag  like the Navy ensign with the lion added. Maybe it belonged to a ship with a lion name?

Megido is in the Jezreel Valley, in the north of Israel, and due to its strategic place saw many battles. In 1918 it was the place of a decisive battle between the British and the Ottomans, and General Alenby won the title Lord of Megido. Also, Megido is thought to be Armageddon.

Nahum Shereshevsky, 3 July 1998

I took a look at the Israeli navy ensign you are wondering about.
The flag does not have stripes and it is not a circle or a lion. The gold thing you saw was the Israel Navy crest. This flag is still in use today. It is the formal flag and is rarely flown.

Ian Shrallow, 30 April 1999

Not so. First, there is strong resemblance between that UFE and one of the Ha'Degel proposals. Which makes me wonder... Second, the GHQ Naval Branch flag (as the GHQ Air Branch flag which I already wrote about) had the Israeli flag in the canton and the Navy symbol at the lower fly. Those Branch flags are not widely used, contrary to the more familiar Air Force flag and the Naval ensign. Third, I don't know about any navy ship in 1948 with a lion as a symbol (and there were not too many of those). The lion is the symbol of the Central Command of the IDF.

Dov Gutterman, 3 May 1999

by Ian Shrallow

Interesting flag. The navy ensign defaced with the navy cap badge. I never saw that flag. I live in Haifa which is the main Israeli navy base so I see most ensigns but never saw this one. The image sent by Ian could be a rank flag. Rank flags and unit/vessel flags are like the naval ensign with an emblem on the lower fly. According to my source (Israel Army History, Ministry of Security) the Naval branch flag is as I described, but who knows... maybe the source is mistaken.

Dov Gutterman, 13 May 1999

Zvi Ruder says that it is the ceremonial colour of Israeli Navy. Makes sense!